We describe the dynamics of a class of second order periodic differential equations whose main feature is a monotone nonlinearity. It is proved that the set of bounded solutions is homeomorphic to the graph of a decreasing function.

In this article, we use critical point theory to obtain multiple periodic solutions for second-order discrete Hamiltonian systems, when the nonlinearity is partially periodic and its gradient is linearly and sublinearly bounded.

We study tree-generating almost linear second-order ACGs that admit bounded nonlinearity either on the context side or on the substructure side, and give distributional learning algorithms for them.

In this paper, we study robust cooperative output regulation problems for a directed network of Lur’e systems that consist of a nominal linear dynamics with an unknown static nonlinearity around it through negative feedback. We assume that the linear part of each agent is identical, but the nonlinearities are allowed to be different for distinct agents. In this sense, the network is heterogeneo...

We investigate the existence and multiplicity of solutions problem − Δ p u q = g ( x , ) in Ω 0 on ∂ where is a smooth, bounded domain ℝ N 1 < ∞, nonlinearity behaves as uq at infinity. use variational methods find multiple minimax critical points associated energy functional. Under suitable assumptions nonlinearity, we cover also resonant case.

This paper considers local stability properties of systems comprising stable linear time-invariant operators in combination with a scalar nonlinearity. We consider those nonlinearities whose gain can be related to the peak value of their input signal. It is assumed that the nonlinearity has some nominal gain for small signals (ie with peak value less than some number), and that the gain then in...

In this paper, we address the problem of event-triggered fuzzy adaptive quantized control for stochastic nonlinear non-affine pure-feedback multi-agent systems. The logic system is used to estimate disturbance term and unknown functions. A nonlinearity decomposition method asymmetric hysteresis quantizer proposed by applying sector bound property. Moreover, reduce communication burden, an proto...

We prove existence and uniqueness results for quasilinear systems of partial differential equations of the form ∂th − ∂ y h = g2 ( y, t, {∂ yh} j=0 ) ∂ y h + g1 ( y, t, {∂ yh} j=0 ) + r(y, t); h(y, 0) = hI(y) for sufficiently large y in a sector in the complex plane, under certain analyticity and decay conditions on h, hI ,g1,g2 and r such that the nonlinearity is formally small as y → ∞. Due t...

It is a well known fact that the nonlinearity of a function f on the n-dimensional vector space Vn is bounded from above by 2 n−1 − 2 1 2 n−1. In cryptographic practice, nonlinear functions are usually constructively obtained in such a way that they support certain mathematical or cryptographic requirements. Hence an important question is how to calculate the nonlinearity of a function when ext...